With little more than a week left before across-the-board federal budget cuts could go into effect, Massachusetts politicians joined scientists and the state’s top health care administrators Monday to offer a grim prognosis of the impact National Institutes of Health spending cuts would have on the Bay State, and Boston in particular.

NIH grants fund hundreds of millions in research annually at the Commonwealth’s hospitals and colleges.

Those research dollars support about 34,000 jobs in Massachusetts, said Dr. Gary Gottlieb, president and chief executive of Partners HealthCare, and about 1,700 could be lost if the automatic cuts slice tens of millions of dollars from state’s share of NIH funding for the remaining months of this year.

If lawmakers in Washington, D.C., do not reach an agreement, the so-called sequester will take effect March 1. Over the course of nine years, projected domestic and defense spending would be slashed by more than $1 trillion.

“The sequester is incredibly stupid for a thousand reasons,” said US Representative Michael E. Capuano of Somerville, who joined Mayor Thomas M. Menino and US Senator Elizabeth Warren in criticizing the impending cuts as senseless and destructive.

Flanked by the health care administrators and scientists, the three Democrats held a news conference Monday morning in the Boston Medical Center pavilion named for Menino.

The research funding cuts could affect the local economy through easy to quantify job losses, they said, and potentially have a long-term impact on the federal budget by curtailing would-be advances.

Warren mentioned research aimed at delaying the onset of Alzheimer’s disease for five years, and said that if such a treatment came to fruition, it could save billions annually in the Medicare and Medicaid budgets.

The federal government, she said, should not tell young scientists they cannot count on sustained research funding.

“It makes no sense,” Warren said. “We can’t build a future this way.”

As of 2011, Boston led all cities in NIH funding for the 17th straight year, according to figures the officials distributed Monday. During that year, the NIH awarded $1.7 billion in grants to Boston’s hospitals and universities, its nonprofits and private companies.

During a meeting in a second-floor conference at the medical center before holding the news conference, the three politicians listened as doctors and administrators explained how their institutions spent NIH research money, and what is at risk of being lost.

Beyond the impact the cuts would have on specific initiatives seeking cures or treatments for illnesses including cancer and diabetes, the administrators cautioned that cutting NIH funding could have a ripple effect and push some of the newest generation of scientists away from research careers.

Funding uncertainties also could persuade scientists to conduct research elsewhere, said Robert Kingston, chief of molecular biology at Massachusetts General Hospital.

He cited the example of a woman he knew about who planned to return to her native Canada, rather than pursue a career in Boston, because of concerns that research dollars might dry up.

When the most talented young scientists “are worried about getting a paycheck, it’s troubling,” Kingston said.

Public research funding forms a pact of trust among patients, researchers, institutions, and the government, said Phillip A. Sharp, an institute professor at the Massachusetts Institute of Technology who in 1993 was awarded the Nobel Prize in medicine.

Once that trust is breached, Sharp said, “they’ll never trust each other again.”

Capuano encouraged the health care officials and scientists to provide him and Warren with specifics. Anecdotes about potential breakthroughs can be difficult to visualize, while jobs lost and the resulting impact on the ill often offers a stark reminder to the public, he said.

“We’ve got to have this conversation nationally,” Warren told those in the conference room.

She asked the administrators and scientists to take the time to “write a letter, send an e-mail, talk to someone. . . . When you’re asked to do an interview, do it, and be specific.”

Menino noted that the scientists and administrators belong to national organizations that include the best in their fields, and he encouraged them to ensure their high-powered groups document cuts that occur under sequestration.

“I don’t know where these elected officials come from,” Menino said of the lawmakers in Washington who appear willing to let the cuts occur, rather than find a compromise.

Treatments that emerge from research begun in Boston, he said later in the news conference, is the sort of thing “you pray for” when tending to an ill loved one.

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